Finite Group DatabasebetaFinite Group Databasebeta| order | 1806 |
| isoclinism | isoclinic class of #14268591 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C43 ⋊ C2×C3 |
| Hall | #11744748 ⋊ C2 |
| Hall | D7×C43 ⋊ C3 |
| Sylow | C43 ⋊ AGL(1,𝔽7) |
| Hall | D7 ⋊ C43⋊C3 |
| Sylow | C7 ⋊ C2×C43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C43 | C2×C3 |
| LCS | G ▷ C7×C43 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 50 |
| transitive degree | μt(G) = 301 |
Polycyclic presentation:
2,3,7,43|c^a=c^6,c^b=c^4,d^b=d^3677 conjugacy classes — view the full character table.
| maximal subgroup of | #14268587⋊C2, C2×#14268591, #27162351, … |
| maximal normal subgroup of | #14268587⋊C2, C2×#14268591, #14268591⋊C7, … |
| maximal quotient of | #16813404, C2×#14268591, #27162351, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1806, 15);